Title:

Mathematical thought from ancient to modern times

Author:

Publication Information:

New York : Oxford University Press, 1990, c1972-

ISBN:

9780195061352

Physical Description:

v. <1, > : ill. ; 23 cm.

Target Audience:

1480 L

Language:

English

Lexile Measure:

1480

Subject Term:

### Available:*

Library | Material Type | Shelf Number | Copies | Status |
---|---|---|---|---|

Searching... Mingus Union High School Library | Book | 510 KLI V.3 | 1 | Searching... Unknown |

Searching... Mingus Union High School Library | Book | 510 KLI V.3 | 1 | Searching... Unknown |

Searching... Mingus Union High School Library | Book | 510 KLI V.3 | 1 | Searching... Unknown |

Searching... Yavapai College (Prescott) Library | Book | QA21.K516 1990 V. 3 | 1 | Searching... Unknown |

Searching... Yavapai College (Verde) Library | Book | QA21.K516 1972 | 1 | Searching... Unknown |

### Bound With These Titles

### On Order

### Summary

### Summary

This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.

### Table of Contents

1 Mathematics in Mesopotamia | p. 3 |

1 Where Did Mathematics Begin? | p. 3 |

2 Political History in Mesopotamia | p. 4 |

3 The Number Symbols | p. 5 |

4 Arithmetic Operations | p. 7 |

5 Babylonian Algebra | p. 8 |

6 Babylonian Geometry | p. 10 |

7 The Uses of Mathematics in Babylonia | p. 11 |

8 Evaluation of Babylonian Mathematics | p. 13 |

2 Egyptian Mathematics | p. 15 |

1 Background | p. 15 |

2 The Arithmetic | p. 16 |

3 Algebra and Geometry | p. 18 |

4 Egyptian Uses of Mathematics | p. 21 |

5 Summary | p. 22 |

3 The Creation of Classical Greek Mathematics | p. 24 |

1 Background | p. 24 |

2 The General Sources | p. 25 |

3 The Major Schools of the Classical Period | p. 27 |

4 The Ionian School | p. 28 |

5 The Pythagoreans | p. 28 |

6 The Eleatic School | p. 34 |

7 The Sophist School | p. 37 |

8 The Platonic School | p. 42 |

9 The School of Eudoxus | p. 48 |

10 Aristotle and His School | p. 51 |

4 Euclid and Apollonius | p. 56 |

1 Introduction | p. 56 |

2 The Background of Euclid's Elements | p. 57 |

3 The Definitions and Axioms of the Elements | p. 58 |

4 Books I to IV of the Elements | p. 60 |

5 Book V: The Theory of Proportion | p. 68 |

6 Book VI: Similar Figures | p. 73 |

7 Books VII, VIII, and IX: The Theory of Numbers | p. 77 |

8 Book X: The Classification of Incommensurables | p. 80 |

9 Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion | p. 81 |

10 The Merits and Defects of the Elements | p. 86 |

11 Other Mathematical Works by Euclid | p. 88 |

12 The Mathematical Work of Apollonius | p. 89 |

5 The Alexandrian Greek Period: Geometry and Trigonometry | p. 101 |

1 The Founding of Alexandria | p. 101 |

2 The Character of Alexandrian Greek Mathematics | p. 103 |

3 Areas and Volumes in the Work of Archimedes | p. 105 |

4 Areas and Volumes in the Work of Heron | p. 116 |

5 Some Exceptional Curves | p. 117 |

6 The Creation of Trigonometry | p. 119 |

7 Late Alexandrian Activity in Geometry | p. 126 |

6 The Alexandrian Period: The Reemergence of Arithmetic and Algebra | p. 131 |

1 The Symbols and Operations of Greek Arithmetic | p. 131 |

2 Arithmetic and Algebra as an Independent Development | p. 135 |

7 The Greek Rationalization of Nature | p. 145 |

1 The Inspiration for Greek Mathematics | p. 145 |

2 The Beginnings of a Rational View of Nature | p. 146 |

3 The Development of the Belief in Mathematical Design | p. 147 |

4 Greek Mathematical Astronomy | p. 154 |

5 Geography | p. 160 |

6 Mechanics | p. 162 |

7 Optics | p. 166 |

8 Astrology | p. 168 |

8 The Demise of the Greek World | p. 171 |

1 A Review of the Greek Achievements | p. 171 |

2 The Limitations of Greek Mathematics | p. 173 |

3 The Problems Bequeathed by the Greeks | p. 176 |

4 The Demise of the Greek Civilization | p. 177 |

9 The Mathematics of the Hindus and Arabs | p. 183 |

1 Early Hindu Mathematics | p. 183 |

2 Hindu Arithmetic and Algebra of the Period A.D. 200-1200 | p. 184 |

3 Hindu Geometry and Trigonometry of the Period A.D. 200-1200 | p. 188 |

4 The Arabs | p. 190 |

5 Arabic Arithmetic and Algebra | p. 191 |

6 Arabic Geometry and Trigonometry | p. 195 |

7 Mathematics circa 1300 | p. 197 |

10 The Medieval Period in Europe | p. 200 |

1 The Beginnings of a European Civilization | p. 200 |

2 The Materials Available for Learning | p. 201 |

3 The Role of Mathematics in Early Medieval Europe | p. 202 |

4 The Stagnation in Mathematics | p. 203 |

5 The First Revival of the Greek Works | p. 205 |

6 The Revival of Rationalism and Interest in Nature | p. 206 |

7 Progress in Mathematics Proper | p. 209 |

8 Progress in Physical Science | p. 211 |

9 Summary | p. 213 |

11 The Renaissance | p. 216 |

1 Revolutionary Influences in Europe | p. 216 |

2 The New Intellectual Outlook | p. 218 |

3 The Spread of Learning | p. 220 |

4 Humanistic Activity in Mathematics | p. 221 |

5 The Clamor for the Reform of Science | p. 223 |

6 The Rise of Empiricism | p. 227 |

12 Mathematical Contributions in the Renaissance | p. 231 |

1 Perspective | p. 231 |

2 Geometry Proper | p. 234 |

3 Algebra | p. 236 |

4 Trigonometry | p. 237 |

5 The Major Scientific Progress in the Renaissance | p. 240 |

6 Remarks on the Renaissance | p. 247 |

13 Arithmetic and Algebra in the Sixteenth and Seventeenth Centuries | p. 250 |

1 Introduction | p. 250 |

2 The Status of the Number System and Arithmetic | p. 251 |

3 Symbolism | p. 259 |

4 The Solution of Third and Fourth Degree Equations | p. 263 |

5 The Theory of Equations | p. 270 |

6 The Binomial Theorem and Allied Topics | p. 272 |

7 The Theory of Numbers | p. 274 |

8 The Relationship of Algebra to Geometry | p. 278 |

14 The Beginnings of Projective Geometry | p. 285 |

1 The Rebirth of Geometry | p. 285 |

2 The Problems Raised by the Work on Perspective | p. 286 |

3 The Work of Desargues | p. 288 |

4 The Work of Pascal and La Hire | p. 295 |

5 The Emergence of New Principles | p. 299 |

15 Coordinate Geometry | p. 302 |

1 The Motivation for Coordinate Geometry | p. 302 |

2 The Coordinate Geometry of Fermat | p. 303 |

3 Rene Descartes | p. 304 |

4 Descartes's Work in Coordinate Geometry | p. 308 |

5 Seventeenth-Century Extensions of Coordinate Geometry | p. 317 |

6 The Importance of Coordinate Geometry | p. 321 |

16 The Mathematization of Science | p. 325 |

1 Introduction | p. 325 |

2 Descartes's Concept of Science | p. 325 |

3 Galileo's Approach to Science | p. 327 |

4 The Function Concept | p. 335 |

17 The Creation of the Calculus | p. 342 |

1 The Motivation for the Calculus | p. 342 |

2 Early Seventeenth-Century Work on the Calculus | p. 344 |

3 The Work of Newton | p. 356 |

4 The Work of Leibniz | p. 370 |

5 A Comparison of the Work of Newton and Leibniz | p. 378 |

6 The Controversy over Priority | p. 380 |

7 Some Immediate Additions to the Calculus | p. 381 |

8 The Soundness of the Calculus | p. 383 |

List of Abbreviations | |

Index |

SD_ILS:272497

9780195061352

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